∠1 and ∠2 are RIGHT ANGLES, VERTICAL ANGLES, and SUPPLEMENTARY ANGLES.
Hope this helps!
Answer:
Hey there!
There is this equation, which states that the angle created by an inscribed angle is half the measure of the arc.
Thus, we can write: 60=5x-5
65=5x
x=13
Let me know if this helps :)
Answer:
![\displaystyle \frac{4}{3}\text{cm}^2/\text{min}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B4%7D%7B3%7D%5Ctext%7Bcm%7D%5E2%2F%5Ctext%7Bmin%7D)
Step-by-step explanation:
<u>Given</u>
<u />![\displaystyle \frac{dV}{dt}=10\:\text{cm}^3/\text{min}\\ \\V=s^3\\\\SA=6s^2\\\\\frac{d(SA)}{dt}=?}\:;s=30\text{cm}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdV%7D%7Bdt%7D%3D10%5C%3A%5Ctext%7Bcm%7D%5E3%2F%5Ctext%7Bmin%7D%5C%5C%20%5C%5CV%3Ds%5E3%5C%5C%5C%5CSA%3D6s%5E2%5C%5C%5C%5C%5Cfrac%7Bd%28SA%29%7D%7Bdt%7D%3D%3F%7D%5C%3A%3Bs%3D30%5Ctext%7Bcm%7D)
<u>Solution</u>
(1) Find the rate of the cube's edge length with respect to time at s=30:
![\displaystyle V=s^3\\\\\frac{dV}{dt}=3s^2\frac{ds}{dt}\\ \\10=3(30)^2\frac{ds}{dt}\\ \\10=3(900)\frac{ds}{dt}\\\\10=2700\frac{ds}{dt}\\\\\frac{10}{2700}=\frac{ds}{dt}\\\\\frac{ds}{dt}=\frac{1}{270}\text{cm}/\text{min}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3Ds%5E3%5C%5C%5C%5C%5Cfrac%7BdV%7D%7Bdt%7D%3D3s%5E2%5Cfrac%7Bds%7D%7Bdt%7D%5C%5C%20%5C%5C10%3D3%2830%29%5E2%5Cfrac%7Bds%7D%7Bdt%7D%5C%5C%20%5C%5C10%3D3%28900%29%5Cfrac%7Bds%7D%7Bdt%7D%5C%5C%5C%5C10%3D2700%5Cfrac%7Bds%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7B10%7D%7B2700%7D%3D%5Cfrac%7Bds%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7Bds%7D%7Bdt%7D%3D%5Cfrac%7B1%7D%7B270%7D%5Ctext%7Bcm%7D%2F%5Ctext%7Bmin%7D)
(2) Find the rate of the cube's surface area with respect to time at s=30:
![\displaystyle SA=6s^2\\\\\frac{d(SA)}{dt}=12s\frac{ds}{dt}\\ \\\frac{d(SA)}{dt}=12(30)\biggr(\frac{1}{270}\biggr)\\\\\frac{d(SA)}{dt}=\frac{360}{270}\biggr\\\\\frac{d(SA)}{dt}=\frac{4}{3}\text{cm}^2/\text{min}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20SA%3D6s%5E2%5C%5C%5C%5C%5Cfrac%7Bd%28SA%29%7D%7Bdt%7D%3D12s%5Cfrac%7Bds%7D%7Bdt%7D%5C%5C%20%5C%5C%5Cfrac%7Bd%28SA%29%7D%7Bdt%7D%3D12%2830%29%5Cbiggr%28%5Cfrac%7B1%7D%7B270%7D%5Cbiggr%29%5C%5C%5C%5C%5Cfrac%7Bd%28SA%29%7D%7Bdt%7D%3D%5Cfrac%7B360%7D%7B270%7D%5Cbiggr%5C%5C%5C%5C%5Cfrac%7Bd%28SA%29%7D%7Bdt%7D%3D%5Cfrac%7B4%7D%7B3%7D%5Ctext%7Bcm%7D%5E2%2F%5Ctext%7Bmin%7D)
Therefore, the surface area increases when the length of an edge is 30 cm at a rate of
.
Answer:
4
Step-by-step explanation:
Since x = 5, you can substitute 5 into the x value of the expression: 5 + 5 - 6. Then, you add the 5 + 5 to get 10 in which you subtract 6 from. The answer is 4.
<h3>
Answer:</h3>
The Area of the tray ≈380 cm
<h3>
Solution:</h3>
- We are given the diameter of the tray, which is equivalent to 22 cm.
- We are asked to find the area of the tray.
- Remember the formula:
- Area of a circle = πr²
- Where
- π -> pi (3.14...)
- r -> radius
- Notice that we aren't given the radius. We're given the diameter only.
- No reason to panic. We can easily find the radius by dividing the diameter by 2.
- The radius is equal to 11 cm.
- Now, plug the values into the formula:
- A=π(11)²
- A=121π
- A≈380 cm
Hope it helps.
Do comment if you have any query.